Subsampling MCMC for Bayesian Variable Selection and Model Averaging in BGNLM

Abstract: Bayesian Generalized Nonlinear Models (BGNLM) offer a flexible nonlinear alternative to GLM while still providing better interpretability than machine learning techniques such as neural networks. In BGNLM, the methods of Bayesian Variable Selection and Model Averaging are applied in an extended GLM setting. Models are fitted to data using MCMC within a genetic framework by an algorithm called GMJMCMC. In this paper, we combine GMJMCMC with a novel algorithm called S-IRLS-SGD for estimating the marginal likelihoods in BGLM/BGNLM by subsampling from the data. This allows to apply GMJMCMC to tall data.